Nonlinear Discrete Dynamical Systems Sketch the graphs of T (x), T 2(x), and T 3(x). How many points are there of periods one, two, and three, respectively?

(b) Let T be the function T : [0, 1] → [0, 1] defined by T (x) =

9 5 x, 0 ≤ x < 1 2 , 9 5 (1 − x), 1 2 ≤ x ≤ 1.

Determine the fixed points of periods one, two, and three.